Quasi-Birth-and-Death Processes, Lattice Path Counting, and Hypergeometric Functions

DOI10.1239/jap/1245676103zbMath1186.60087OpenAlexW2130398494MaRDI QIDQ5321765

Mark S. Squillante, Johan S. H. van Leeuwaarden, Erik M. M. Winands

Publication date: 15 July 2009

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/jap/1245676103

zbMATH Keywords

hypergeometric functionmatrix-analytic methodsquasi-birth-and-death processlattice path countingrate matrix

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items

EXPLICIT SOLUTIONS FOR CONTINUOUS-TIME QBD PROCESSES BY USING RELATIONS BETWEEN MATRIX GEOMETRIC ANALYSIS AND THE PROBABILITY GENERATING FUNCTIONS METHOD ⋮ The snowball effect of customer slowdown in critical many-server systems ⋮ On lattice path counting and the random product representation, with applications to the \(E_r/M/1\) queue and the \(M/E_r/1\) queue ⋮ Bi-objective optimization of a queueing model with two-phase heterogeneous service ⋮ Stationary analysis of the shortest queue problem ⋮ A comparative analysis of the successive lumping and the lattice path counting algorithms ⋮ A polling system with `join the shortest -- serve the longest' policy ⋮ Performance analysis and optimization of a retrial queue with working vacations and starting failures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analysis of a simple Markovian re-entrant line with infinite supply of work under the LBFS policy
• A general class of Markov processes with explicit matrix-geometric solutions
• A two-queue, one-server model with priority for the longer queue
• Combining make to order and make to stock
• Priority queues
• The Longer Queue Model
• Quasi-Birth-and-Death Processes with an Explicit Rate Matrix
• Operator-geometric stationary distributions for markov chains, with application to queueing models
• A bernoulli excursion and its various applications
• Introduction to Matrix Analytic Methods in Stochastic Modeling
• A Queueing Model to Analyze the Value of Centralized Inventory Information